Rather than wait for outside pressure, Majority Leader Mitch McConnell said Tuesday the statue of Jefferson Davis prominently displayed in Kentucky's state capitol should be moved to a museum — but he wasn't quite ready to propose moving the Jefferson Davis statue out of the U.S. Capitol.

The Kentucky Republican noted Davis' sole link to the Bluegrass State is he was born there, but then moved to Mississippi and went on to become the president of the Confederate States of America.

"I think it's appropriate certainly in Kentucky to be talking about the appropriateness of continuing to have Jefferson Davis' statue in a very prominent place in our state capitol," McConnell said. "Maybe a better place for that would be the Kentucky History Museum, which is also in the state capitol."

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Earlier on Tuesday, the Republican nominee for governor of Kentucky, Matt Bevin, who also ran against McConnell in his last reelection campaign, also called for the removal of the statue.

McConnell did not take a position on the Jefferson Davis statue in Statuary Hall in the U.S. Capitol, or those of other Confederate leaders, saying he was unsure what statues actually existed.

Reid then at his weekly press conference said the law makes it clear states choose their own statues.

"That really is up to the states," he said, although he said they would "make sure the states know who they have here."

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Separately, he said the statue of Nevada Sen. Pat McCarran should be "put out to pasture somewhere. He doesn't represent the things our country stands for."

He added, "The statues are important. They really send a message."

There are a number of other statues of Confederates in the Capitol, including Robert E. Lee, one of Virginia's two statues (the other is George Washington), and Alexander Hamilton Stephens, who served as the vice president of the Confederacy among other positions and represents Georgia in the Capitol.